Related papers: Numerical verification of solutions for nonlinear …
We propose a robust numerical method to find the coefficient of the creation or depletion term of parabolic equations from the measurement of the lateral Cauchy information of their solutions. Most papers in the field study this nonlinear…
We provide an accurate verification method for solutions of heat equations with a superlinear nonlinearity. The verification method numerically proves the existence and local uniqueness of the exact solution in a neighborhood of a…
We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a result has previously been studied only for certain…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove…
The purpose of the present work is to study the existence of solutions to initial value problems for nonlinear first order differential systems with nonlinear nonlocal boundary conditions of functional type. The existence results are…
In this article we derive a priori error estimates for the $hp$-version of the mortar finite element method for parabolic initial-boundary value problems. Both semidiscrete and fully discrete methods are analysed in $L^2$- and $H^1$-norms.…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
The primary objective of this work is to establish pointwise gradient estimates for solutions to a class of parabolic nonlinear nonlocal measure data problems, expressed in terms of caloric Riesz potentials of the data. As a consequence of…
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
We investigate pointwise upper bounds for nonnegative solutions $u(x,t)$ of the nonlinear initial value problem \begin{equation}\label{0.1} 0\leq(\partial_t-\Delta)^\alpha u\leq u^\lambda \quad\text{ in }\mathbb{R}^n…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
In this paper we study the quasilinear nondiagonal parabolic type systems. We assume that the principal elliptic operator, which is part of the parabolic system, has a divergence structure. Under certain conditions it is proved the…
We study the following ultraparabolic equation \[ \frac{\partial}{\partial t}u\left(t,s\right)+\frac{\partial}{\partial…
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and on the investigation of differential and certain qualitative…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
In this paper, we are concerned with the first initial boundary value problem for a class of fully nonlinear parabolic equations on Riemannian manifolds. As usual, the establishment of the a priori C^2 estimates is our main part. Based on…
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…